Throat distribution for a rotor and rotor blade having camber and location of local maximum thickness distribution

ABSTRACT

A rotor blade for a compressor of a gas turbine engine includes an airfoil. The airfoil has a span that extends from 0% at the root to 100% at the tip and a mean camber line that extends from a leading edge to a trailing edge. The airfoil has a location of local maximum thickness defined as a ratio of a first arc distance along the mean camber line between the leading edge and a position of the local maximum thickness to a total arc distance along the mean camber line from the leading edge to the trailing edge. A value of the ratio increases from the root to a first position value, decreases from the first position value to a second position value and increases from the second position value to the tip. The first position value is at a spanwise location within 20% to 50% of the span.

TECHNICAL FIELD

The present disclosure generally relates to gas turbine engines, andmore particularly relates to a rotor having a throat distribution thatresults in increased flow capacity, and a rotor blade for a rotor havinga camber distribution that reduces flutter and a location of localmaximum thickness distribution that provides robustness.

BACKGROUND

Gas turbine engines may be employed to power various devices. Forexample, a gas turbine engine may be employed to power a mobileplatform, such as an aircraft. Generally, gas turbine engines includecompressor and fan axial rotors, which are operable to increase thestatic pressure of the gas flowing within the gas turbine engine or todraw air into the gas turbine engine, respectively. Thus, typically,compressor and fan axial rotors are designed to enable large flowcapacity, while being subject to packaging, weight, performance,operability, and durability constraints. In certain instances, in orderto enable a large flow capacity, compressor and fan rotors may besubject to reduced efficiency, reduced flutter margin and reducedrobustness.

Further, rotor blades for use with rotors, such as compressors or fanaxial rotors for a gas turbine engine powering a mobile platform, may besubject to weight constraints. In certain instances, reducing a weightof the rotor blade may result in airfoils with lower natural vibratoryfrequencies that tend to flutter more easily. In addition to theintended working gas flows, components of the gas turbine engine may, incertain instances, encounter foreign object(s) during operation. Inthese instances, the components of the gas turbine engine may berequired to continue to operate after this encounter or may be requiredto shut down safely. In the example of a rotor blade for a fan axialrotor, the rotor blade may be required to withstand the encounter withminimal permanent deformation. Generally, in order to ensure the rotorblade withstands the encounter, an airfoil of the rotor blade may havean increased overall thickness to provide robustness to the airfoil. Theincreased overall thickness, however, increases the weight of theairfoil, and thus, the rotor blade, which is undesirable for theoperation of the gas turbine engine.

Accordingly, it is desirable to provide a rotor, such as a compressor orfan axial rotor, with a throat distribution that provides large flowcapacity without reducing efficiency of the rotor and without reducing aflutter margin. Moreover, it is desirable to provide a rotor blade thathas a reduced weight and a camber distribution that results in a reducedtendency to flutter. Further, it is desirable to provide a rotor bladethat has a location of local maximum thickness distribution that reducesthe weight of the rotor blade and maintains high efficiency, whileproviding robustness to the rotor blade should the rotor blade encountera foreign object during operation. Furthermore, other desirable featuresand characteristics of the present invention will become apparent fromthe subsequent detailed description and the appended claims, taken inconjunction with the accompanying drawings and the foregoing technicalfield and background.

SUMMARY

According to various embodiments, provided is a rotor for a compressor.The rotor includes a hub and a plurality of airfoils having a root, atip opposite the root and a span that extends from 0% at the root to100% at the tip. Each of the plurality of airfoils is coupled to the hubat the root and is spaced apart from adjacent ones of the plurality ofairfoils over the span by a throat dimension defined between theadjacent ones of the plurality of airfoils. The throat dimension has amaximum value at a spanwise location between 60% of the span and 90% ofthe span of the adjacent ones of the plurality of airfoils, and at 10%of the span of the adjacent ones of the plurality of airfoils above orbelow the spanwise location of the maximum value, the throat dimensionis less than 97% of the maximum value. The throat dimension at 5% of thespan of the adjacent ones of the plurality of airfoils is less than 70%of the maximum value.

Further provided according to various embodiments is a rotor for acompressor. The rotor includes a hub and a plurality of airfoils havinga root, a tip opposite the root and a span that extends from 0% at theroot to 100% at the tip. Each of the plurality of airfoils is coupled tothe hub at the root and is spaced apart from adjacent ones of theplurality of airfoils over the span by a throat dimension definedbetween the adjacent ones of the plurality of airfoils. The throatdimension has a maximum value at a spanwise location between 60% of thespan and 90% of the span of the adjacent ones of the plurality ofairfoils, and at 10% of the span of the adjacent ones of the pluralityof airfoils above and below the spanwise location of the maximum value,the throat dimension is less than 97% of the maximum value. The throatdimension between 90% of the span and the tip of the adjacent ones ofthe plurality of airfoils has a first value, and the throat dimensionbetween the root and 10% of the span of the adjacent ones of theplurality of airfoils has a second value that is less than 60% of themaximum value.

Also provided is a rotor for a compressor. The rotor includes a hub anda plurality of airfoils having a root, a tip opposite the root and aspan that extends from 0% at the root to 100% at the tip. Each of theplurality of airfoils is coupled to the hub at the root and is spacedapart from adjacent ones of the plurality of airfoils over the span by athroat dimension defined between the adjacent ones of the plurality ofairfoils. The throat dimension has a maximum value at a spanwiselocation between 60% of the span and 90% of the span of the adjacentones of the plurality of airfoils, and at 10% of the span of theadjacent ones of the plurality of airfoils above and below the spanwiselocation of the maximum value, the throat dimension is less than 97% ofthe maximum value. The throat dimension between 90% of the span and thetip of the adjacent ones of the plurality of airfoils has a first value,the throat dimension between the root and 10% of the span of theadjacent ones of the plurality of airfoils has a second value that isless than 70% of the maximum value and the second value is less than thefirst value.

According to various embodiments, provided is a rotor blade for acompressor of a gas turbine engine. The rotor blade includes an airfoilthat extends from a root to a tip and has a leading edge and a trailingedge. The airfoil has a span that extends from 0% at the root to 100% atthe tip and a mean camber line that extends from the leading edge to thetrailing edge. The airfoil includes a total camber distribution thatincreases from the root to a maximum value of total camber between 5% ofthe span and 20% of the span.

Also provided is a rotor blade for a compressor of a gas turbine engine.The rotor blade includes an airfoil that extends from a root to a tipand has a leading edge and a trailing edge. The airfoil has a span thatextends from 0% at the root to 100% at the tip and a mean camber linethat extends from the leading edge to the trailing edge. The airfoilincludes a total camber distribution of a total camber of the meancamber line. The total camber has a first value at the root, a maximumvalue between 5% of the span and 20% of the span and the total camberhas a second value at the tip, which is less than the first value andthe maximum value.

Further provided is a rotor for a compressor of a gas turbine engine.The rotor includes a hub and an airfoil extending from a root to a tipand having a leading edge and a trailing edge. The airfoil is coupled tothe hub at the root, the airfoil having a span that extends from 0% atthe root to 100% at the tip and a mean camber line that extends from theleading edge to the trailing edge. The airfoil has a total camberdistribution of a total camber of the mean camber line. The total camberhas a first value at the root, a maximum value between 5% of the spanand 20% of the span and the total camber distribution decreases from themaximum value to at least 80% of the span of the airfoil.

According to various embodiments, a rotor blade for a compressor of agas turbine engine is provided. The rotor blade includes an airfoilextending from a root to a tip and having a leading edge and a trailingedge. The airfoil has a span that extends from 0% at the root to 100% atthe tip and a mean camber line that extends from the leading edge to thetrailing edge. The airfoil has a location of local maximum thicknessdefined as a ratio of a first arc distance along the mean camber linebetween the leading edge and a position of the local maximum thicknessto a total arc distance along the mean camber line from the leading edgeto the trailing edge. A value of the ratio increases from the root to afirst position value, decreases from the first position value to asecond position value and increases from the second position value tothe tip. The first position value is at a spanwise location within 20%to 50% of the span.

Also provided is a rotor blade for a compressor of a gas turbine engine.The rotor blade includes an airfoil extending from a root to a tip andhaving a leading edge and a trailing edge. The airfoil has a span thatextends from 0% at the root to 100% at the tip and a mean camber linethat extends from the leading edge to the trailing edge. The airfoil hasa location of local maximum thickness defined as a ratio of a first arcdistance along the mean camber line between the leading edge and aposition of the local maximum thickness to a total arc distance alongthe mean camber line from the leading edge to the trailing edge. A valueof the ratio increases from a position value at the root to a firstposition value, decreases from the first position value to a secondposition value and increases from the second position value to a thirdposition value at the tip. The second position value is within 60% to90% of the span.

Further provided is a rotor for a compressor of a gas turbine engine.The rotor includes a hub and an airfoil extending from a root to a tipand having a leading edge and a trailing edge. The airfoil has a spanthat extends from 0% at the root to 100% at the tip and a mean camberline that extends from the leading edge to the trailing edge. Theairfoil has a location of local maximum thickness defined as a ratio ofa first arc distance along the mean camber line between the leading edgeand a position of the local maximum thickness to a total arc distancealong the mean camber line from the leading edge to the trailing edge. Avalue of the ratio increases from a position value at the root to afirst position value, decreases from the first position value to asecond position value and increases from the second position value to athird position value at the tip. The position value is an absoluteminimum value of the ratio over the span of the airfoil and the secondposition value is at a spanwise location within 60% to 90% of the span.

DESCRIPTION OF THE DRAWINGS

The exemplary embodiments will hereinafter be described in conjunctionwith the following drawing figures, wherein like numerals denote likeelements, and wherein:

FIG. 1 is a schematic cross-sectional illustration of a gas turbineengine, which includes an exemplary rotor and rotor blade in accordancewith the various teachings of the present disclosure;

FIG. 2 is a front view of a rotor of a fan section of the gas turbineengine of FIG. 1, in which the rotor has a throat distribution thatresults in increased flow capacity and includes a rotor blade that has atotal camber distribution that reduces flutter and a location of localmaximum thickness distribution that provides robustness to foreignobject encounters;

FIG. 3 is a schematic cross-sectional view of the rotor of FIG. 2, takenalong line 2-2 of FIG. 2, which illustrates one of the rotor bladesassociated with the rotor of FIG. 2, in which the rotor has a throatdistribution that results in increased flow capacity;

FIG. 4 is a cross-sectional view of the rotor blade of FIG. 3, takenalong line 4-4 of FIG. 3;

FIG. 5 is a graph of normalized throat (throat dimension divided bymaximum throat dimension; abscissa) versus percent span (ordinate)illustrating a spanwise throat distribution associated with the rotor ofFIG. 2;

FIG. 5A is a graph of normalized throat (throat dimension divided byaverage throat dimension; abscissa) versus percent span (ordinate)illustrating a spanwise throat distribution associated with the rotor ofFIG. 2;

FIG. 6 is a cross-sectional view of two adjacent rotor blades of therotor of FIG. 2, taken along an arc length (tangential direction) of therotor starting from line 6-6 of FIG. 3, which illustrates a first valuefor the throat dimension at a spanwise location between 90% and 100% ofthe span of the rotor blades;

FIG. 7 is a cross-sectional view of two adjacent rotor blades of therotor of FIG. 2, taken along an arc length (tangential direction) of therotor starting from the perspective of line 7-7 of FIG. 3, whichillustrates a second value for the throat dimension at a spanwiselocation between 0% and 10% of the span of the rotor blades;

FIG. 8 is a cross-sectional view of two adjacent rotor blades of therotor of FIG. 2, taken along an arc length (tangential direction) of therotor starting from the perspective of 8-8 of FIG. 3, which illustratesa maximum value for the throat dimension at a spanwise location between60% and 90% of the span of the rotor blades;

FIG. 9 is a cross-sectional view of two adjacent rotor blades of therotor of FIG. 2, taken along an arc length (tangential direction) of therotor starting from the perspective of line 9-9 of FIG. 3, whichillustrates a third value for the throat dimension at a spanwiselocation that is 10% above the spanwise location of the maximum valuefor the throat dimension;

FIG. 10 is a cross-sectional view of two adjacent rotor blades of therotor of FIG. 2, taken along an arc length (tangential direction) of therotor starting from the perspective of line 10-10 of FIG. 3, whichillustrates a fourth value for the throat dimension at a spanwiselocation that is 10% below the spanwise location of the maximum valuefor the throat dimension;

FIG. 11 is a schematic cross-sectional view of the rotor of FIG. 2,taken along line 2-2 of FIG. 2, which illustrates another exemplary oneof the rotor blades associated with the rotor of FIG. 2 that has a totalcamber distribution that reduces flutter;

FIG. 12 is a cross-sectional view of the rotor blade of FIG. 11, takenalong line 12-12 of FIG. 11;

FIG. 13 is a graph of total camber (in degrees; abscissa) versus percentspan (ordinate) illustrating two exemplary spanwise total camberdistributions associated with the rotor blade of FIG. 11;

FIG. 14 is a cross-sectional view of the rotor blade of FIG. 11, takenalong line 14-14 of FIG. 11, which illustrates a total camber of therotor blade at a spanwise location between 0% of the span and 5% of thespan;

FIG. 15 is a cross-sectional view of the rotor blade of FIG. 11, takenalong line 15-15 of FIG. 11, which illustrates a total camber of therotor blade at a spanwise location between 5% of the span and 20% of thespan;

FIG. 16 is a cross-sectional view of the rotor blade of FIG. 11, takenalong line 16-16 of FIG. 11, which illustrates a total camber of therotor blade at a spanwise location between 20% of the span and 30% ofthe span;

FIG. 17 is an overlay of the cross-sectional views of FIGS. 14-16, whichillustrates a portion of the total camber distribution of the rotorblade;

FIG. 18 is a schematic cross-sectional illustration of a portion of thegas turbine engine of FIG. 1, which includes a rotor having a hub slopeangle and a plurality of rotor blades with a total camber distributionthat reduces flutter;

FIG. 19 is a schematic cross-sectional view of the rotor of FIG. 2,taken along line 2-2 of FIG. 2, which illustrates another exemplary oneof the rotor blades associated with the rotor of FIG. 2 that has alocation of local maximum thickness distribution that providesrobustness to foreign object encounters;

FIG. 20 is a cross-sectional view of the rotor blade of FIG. 19, takenalong line 20-20 of FIG. 19;

FIG. 21 is a graph of location of local maximum thickness (LMT;abscissa) versus percent span (ordinate) illustrating two exemplaryspanwise location of local maximum thickness distributions associatedwith the rotor blade of FIG. 19;

FIG. 22 is a cross-sectional view of the rotor blade of FIG. 19, takenalong line 22-22 of FIG. 19, which illustrates a value of the locationof local maximum thickness of the rotor blade at a spanwise locationbetween 0% of the span and 10% of the span;

FIG. 23 is a cross-sectional view of the rotor blade of FIG. 19, takenalong line 23-23 of FIG. 19, which illustrates a value of the locationof local maximum thickness of the rotor blade at a spanwise locationbetween 20% of the span and 50% of the span;

FIG. 24 is a cross-sectional view of the rotor blade of FIG. 19, takenalong line 24-24 of FIG. 19, which illustrates a value of the locationof local maximum thickness of the rotor blade at a spanwise locationbetween 60% of the span and 90% of the span;

FIG. 25 is a cross-sectional view of the rotor blade of FIG. 19, takenalong line 25-25 of FIG. 19, which illustrates a value of the locationof local maximum thickness of the rotor blade at a spanwise locationbetween 90% of the span and 100% of the span;

FIG. 26 is an overlay of the cross-sectional views of FIGS. 22 and 23,which illustrates a difference between the values of the location oflocal maximum thickness for a portion of the location of local maximumthickness distribution of the rotor blade;

FIG. 27 is an overlay of the cross-sectional views of FIGS. 23 and 24,which illustrates a difference between the values of the location oflocal maximum thickness for a portion of the location of local maximumthickness distribution of the rotor blade; and

FIG. 28 is an overlay of the cross-sectional views of FIGS. 24 and 25,which illustrates a difference between the values of the location oflocal maximum thickness for a portion of the location of local maximumthickness distribution of the rotor blade.

DETAILED DESCRIPTION

The following detailed description is merely exemplary in nature and isnot intended to limit the application and uses. Furthermore, there is nointention to be bound by any expressed or implied theory presented inthe preceding technical field, background, brief summary or thefollowing detailed description. In addition, those skilled in the artwill appreciate that embodiments of the present disclosure may bepracticed in conjunction with any type of rotor that would benefit froman increased flow capacity without reducing efficiency or fluttermargin, and the rotor described herein for a compressor or fan axialrotor is merely one exemplary embodiment according to the presentdisclosure. Further, those skilled in the art will appreciate thatembodiments of the present disclosure may be practiced in conjunctionwith any type of blade that would benefit from a reduced weight withoutreducing flutter margin, and the rotor blade described herein for usewith a compressor or fan axial rotor is merely one exemplary embodimentaccording to the present disclosure. Moreover, those skilled in the artwill appreciate that embodiments of the present disclosure may bepracticed in conjunction with any type of blade that would benefit froman increased robustness without increasing the weight of the blade, andthe rotor blade described herein for use with a compressor or fan axialrotor is merely one exemplary embodiment according to the presentdisclosure. In addition, while the rotor and rotor blade are describedherein as being used with a gas turbine engine onboard a mobileplatform, such as a bus, motorcycle, train, motor vehicle, marinevessel, aircraft, rotorcraft and the like, the various teachings of thepresent disclosure can be used with a gas turbine engine on a stationaryplatform. Further, it should be noted that many alternative oradditional functional relationships or physical connections may bepresent in an embodiment of the present disclosure. In addition, whilethe figures shown herein depict an example with certain arrangements ofelements, additional intervening elements, devices, features, orcomponents may be present in an actual embodiment. It should also beunderstood that the drawings are merely illustrative and may not bedrawn to scale.

As used herein, the term “axial” refers to a direction that is generallyparallel to or coincident with an axis of rotation, axis of symmetry, orcenterline of a component or components. For example, in a cylinder ordisc with a centerline and generally circular ends or opposing faces,the “axial” direction may refer to the direction that generally extendsin parallel to the centerline between the opposite ends or faces. Incertain instances, the term “axial” may be utilized with respect tocomponents that are not cylindrical (or otherwise radially symmetric).For example, the “axial” direction for a rectangular housing containinga rotating shaft may be viewed as a direction that is generally parallelto or coincident with the rotational axis of the shaft. Furthermore, theterm “radially” as used herein may refer to a direction or arelationship of components with respect to a line extending outward froma shared centerline, axis, or similar reference, for example in a planeof a cylinder or disc that is perpendicular to the centerline or axis.In certain instances, components may be viewed as “radially” alignedeven though one or both of the components may not be cylindrical (orotherwise radially symmetric). Furthermore, the terms “axial” and“radial” (and any derivatives) may encompass directional relationshipsthat are other than precisely aligned with (e.g., oblique to) the trueaxial and radial dimensions, provided the relationship is predominatelyin the respective nominal axial or radial direction. As used herein, theterm “transverse” denotes an axis that crosses another axis at an anglesuch that the axis and the other axis are neither substantiallyperpendicular nor substantially parallel.

With reference to FIG. 1, a partial, cross-sectional view of anexemplary gas turbine engine 100 is shown with the remaining portion ofthe gas turbine engine 100 being generally axisymmetric about alongitudinal axis 140, which also comprises an axis of rotation for therotating components in the gas turbine engine 100. In the depictedembodiment, the gas turbine engine 100 is an annular multi-spoolturbofan gas turbine jet engine within an aircraft 99, although otherarrangements and uses may be provided. As will be discussed herein, withbrief reference to FIG. 2, the gas turbine engine 100 includes a rotor200 including a plurality of rotor blades 204 that have a throatdistribution or throat dimension distribution. By providing the throatdimension distribution of the present disclosure, the rotor 200 has anincreased flow capacity while maintaining an efficiency and fluttermargin of the rotor 200. In one example, the flow capacity of the rotor200 may be increased by about 2% or more as compared to a conventionalrotor. As will be discussed herein, with brief reference to FIG. 11, thegas turbine engine 100 also includes the rotor 200, which may include aplurality of rotor blades 300, with each of the rotor blades 300 havinga total camber distribution 302 that reduces flutter. The rotor blade300 of FIG. 11 reduces a susceptibility to flutter by modifying the modeshape of the rotor blade 300, which changes a fundamental vibratory modeof the rotor blade 300. As discussed with regard to FIGS. 11-17, therotor blade 300 has a mode shape that is modified to be less susceptibleto flutter by decreasing a total camber of the rotor blade 300 near andat a root of the rotor blade 300. With brief reference to FIG. 19, thegas turbine engine 100 includes the rotor 200, which may include aplurality of rotor blades 500, with each of the rotor blades 500 havinga location of local maximum thickness distribution 502 that providesrobustness to foreign object encounters without increasing a weight ofthe rotor blades 500. In addition, the location of local maximumthickness distribution provides robustness without reducing the flowcapacity and efficiency of the rotor 200. Stated another way, byproviding each of the rotor blades 500 with the location of localmaximum thickness distribution, the rotor blades 500 have materialpositioned where it may reduce permanent deformation due to foreignobject encounters, without increasing the weight of the rotor blades 500or reducing flow capacity or efficiency of the rotor 200. Further, itshould be understood that while the rotor blades 204, 300, 500 aredescribed and illustrated herein as comprising separate and discreterotor blades 204, 300, 500, each of the rotor blades 300, 500 may bearranged to have the throat dimension distribution of the rotor blades204. Moreover, each of the rotor blades 300 may include the location oflocal maximum thickness distribution as discussed with regard to therotor blades 500, and each of the rotor blades 500 may include the totalcamber distribution 302 discussed with regard to the rotor blades 300.Thus, the rotor 200 may include a plurality of rotor blades whichinclude one or more of a throat dimension distribution for increasedflow capacity, a total camber distribution for increased flutter marginand a location of local maximum thickness distribution for improvedrobustness without a weight increase.

In this example, with reference back to FIG. 1, the gas turbine engine100 includes fan section 102, a compressor section 104, a combustorsection 106, a turbine section 108, and an exhaust section 110. In oneexample, the fan section 102 includes the rotor 200 having a pluralityof rotor blades 204, 300, 500, which draw air into the gas turbineengine 100 and accelerate it. A fraction of the accelerated airexhausted from the rotor 200 is directed through an outer (or first)bypass duct 116 and the remaining fraction of air exhausted from therotor 200 is directed into the compressor section 104. The outer bypassduct 116 is generally defined by an inner casing 118 and an outer casing144. In the embodiment of FIG. 1, the compressor section 104 includes anintermediate pressure compressor 120 and a high pressure compressor 122.However, in other embodiments, the number of compressors in thecompressor section 104 and the configuration thereof may vary. One ormore of the intermediate pressure compressor 120 and the high pressurecompressor 122 may also include the rotor 200. In the depictedembodiment, the intermediate pressure compressor 120 and the highpressure compressor 122 sequentially raise the pressure of the air anddirect a majority of the high pressure air into the combustor section106. A fraction of the compressed air bypasses the combustor section 106and is used to cool, among other components, turbine blades in theturbine section 108.

In the embodiment of FIG. 1, in the combustor section 106, whichincludes a combustion chamber 124, the high pressure air is mixed withfuel, which is combusted. The high-temperature combustion air isdirected into the turbine section 108. In this example, the turbinesection 108 includes three turbines disposed in axial flow series,namely, a high pressure turbine 126, an intermediate pressure turbine128, and a low pressure turbine 130. However, it will be appreciatedthat the number of turbines, and/or the configurations thereof, mayvary. In this embodiment, the high-temperature air from the combustorsection 106 expands through and rotates each turbine 126, 128, and 130.As the turbines 126, 128, and 130 rotate, each drives equipment in thegas turbine engine 100 via concentrically disposed shafts or spools. Inone example, the high pressure turbine 126 drives the high pressurecompressor 122 via a high pressure shaft 134, the intermediate pressureturbine 128 drives the intermediate pressure compressor 120 via anintermediate pressure shaft 136, and the low pressure turbine 130 drivesthe rotor 200 via a low pressure shaft 138.

Rotor Throat Distribution

With reference to FIG. 2, the rotor 200 is shown in greater detail. Inthe example of FIG. 2, the rotor 200 is a fan axial rotor. The rotor 200includes a rotor disk 202 and in this example, the plurality of rotorblades 204, 300, 500. With reference to FIG. 3, one of the plurality ofrotor blades 204 for use with the rotor 200 of the gas turbine engine100 is shown. Each of the rotor blades 204 may be referred to as an“airfoil 204.” The airfoils 204 extend in a radial direction (relativeto the longitudinal axis 140 of the gas turbine engine 100) about theperiphery of the rotor disk 202. The airfoils 204 each include a leadingedge 206, an axially-opposed trailing edge 208, a base or root 210, anda radially-opposed tip 212. The tip 212 is spaced from the root 210 in ablade height, span or spanwise direction, which generally corresponds tothe radial direction or R-axis of a coordinate legend 211 in the view ofFIG. 3. In this regard, the radial direction or R-axis is radiallyoutward and orthogonal to the axial direction or X-axis, and the axialdirection or X-axis is parallel to the longitudinal axis 140 or axis ofrotation of the gas turbine engine 100. A tangential direction or T-axisis mutually orthogonal to the R-axis and the X-axis.

As shown in FIG. 3, the span S of each of the airfoils 204 is 0% at theroot 210 (where the airfoil 204 is coupled to a rotor hub 222) and is100% at the tip 212. In this example, the airfoils 204 are arranged in aring or annular array surrounded by a static fan shroud 216. The staticfan shroud 216 is, in turn, circumscribed by an annular housing piece218 defining a containment pocket 220. The airfoils 204 and the rotordisk 202 are generally composed of a metal, metal alloy or apolymer-based material, such as a polymer-based composite material. Inone example, the airfoils 204 are integrally formed with the rotor disk202 as a monolithic or single piece structure commonly referred to as abladed disk or “blisk.” In other examples, the airfoils 204 may beinsert-type blades, which are received in mating slots provided aroundthe outer periphery of rotor disk 202. In still further examples, therotor 200 may have a different construction. Generally, then, it shouldbe understood that the rotor 200 is provided by way of non-limitingexample and that the rotor 200 (and the airfoils 204 described herein)may be fabricated utilizing various different manufacturing approaches.Such approaches may include, but are not limited to, casting andmachining, three dimensional metal printing processes, direct metallaser sintering, Computer Numerical Control (CNC) milling of a preformor blank, investment casting, electron beam melting, binder jetprinting, powder metallurgy and ply lay-up, to list but a few examples.Regardless of its construction, the rotor 200 includes a rotor hub 222defining a hub flow path. The hub flow path extends over the outersurface of the rotor disk 202 and between the airfoils 204 to guideairflow along from the inlet end (inducer or leading edge) to the outletend (exducer or trailing edge) of the rotor 200. As shown in FIG. 3,each of the plurality of airfoils 204 is coupled to the rotor hub 222 atthe root 210 (0% span). It should be noted that while each of theplurality of airfoils 204 are illustrated herein as being coupled to therotor hub 222 at an angle relative to the axial direction (A-axis), oneor more of the plurality of airfoils 204 may be coupled to the rotor hub222 along a straight line. Further, it should be noted that one or moreof the plurality of airfoils 204 may be coupled to the rotor hub 222along a complex curved surface. It should be noted that in the instanceswhere the plurality of airfoils 204 are coupled to the rotor hub 222 atan angle, the span remains at 0% at the root 210. In other words, thespan of each of the plurality of airfoils 204 remains at 0% at the root210 regardless of the shape of the rotor hub 222.

With reference to FIG. 4, each of the airfoils 204 further includes afirst principal face or a “pressure side” 224 and a second, opposingface or a “suction side” 226. The pressure side 224 and the suction side226 extend in a chordwise direction along a chord line CH and areopposed in a thickness direction normal to a mean camber line 228, whichis illustrated as a dashed line in FIG. 4 that extends from the leadingedge 206 to the trailing edge 208. The pressure side 224 and the suctionside 226 extend from the leading edge 206 to the trailing edge 208. Inone example, each of the airfoils 204 is somewhat asymmetrical andcambered along the mean camber line 228. The pressure side 224 has acontoured, generally concave surface geometry, which gently bends orcurves in three dimensions. The suction side 226 has a contoured,generally convex surface geometry, which likewise bends or curves inthree dimensions. In other embodiments, the airfoils 204 may not becambered and may be either symmetrical or asymmetrical.

With reference back to FIG. 2, as shown, the rotor 200 includes multipleairfoils 204, 300, 500 which are spaced about a rotor rotational axis214. The rotor rotational axis 214 is substantially parallel to andcollinear with the longitudinal axis 140 of the gas turbine engine 100.In the example of the airfoils 204, each one of the airfoils 204 isspaced apart from an adjacent one of the plurality of airfoils 204 by athroat dimension distribution 240, which varies along the span S of theairfoils 204. As used herein “throat dimension” is defined as a minimumphysical distance between adjacent airfoils 204 at a particular spanwiselocation or a particular location along the span of the adjacentairfoils 204. In one example, with reference to FIG. 5, a graph showsthe variation of the normalized throat dimension distribution 240 alongthe span S of the airfoils 204. In FIG. 5, the abscissa or horizontalaxis 236 is a normalized value of the throat dimension, which isnormalized by dividing the throat dimension at the particular spanwiselocation by a maximum throat dimension (maximum value 246) betweenadjacent ones of the airfoils 204 along the entirety of the span of theairfoils 204 (and the normalized throat dimension may be multiplied by100 to arrive at a percentage of the maximum value 246); and theordinate or vertical axis 238 is the spanwise location or location alongthe span of the adjacent airfoils 204 (span is 0% at the root 210 (FIG.3) and span is 100% at the tip 212 (FIG. 3)). In one example, thenormalized value of the throat dimension ranges from about 0.46 to 1,with 1 representing the location of the maximum value 246 for the throatdimension.

As shown in FIG. 5, the throat dimension between 90% of the span and100% of the span of the adjacent ones of the plurality of airfoils 204has a first value 242. In one example, the first value 242 is about 0.5(50%) to about 0.7 (70%) of the maximum value 246 of the throatdimension distribution 240. With reference to FIG. 6, a first throatdimension 280 is shown as defined between adjacent ones of the airfoils204. FIG. 6 is a cross-sectional view through two adjacent airfoils 204,taken along an arc length (in the tangential direction or along theT-axis) of the rotor 200 starting from line 6-6 of FIG. 3 into the page.As shown in FIG. 6, the first throat dimension 280 of the throatdimension distribution 240 is defined as the minimum physical distancebetween the two airfoils 204 at a spanwise location between 90% of thespan and 100% of the span, and in the example of FIG. 6 the first throatdimension 280 is at the tip 212 or 100% span. The first throat dimension280 is divided by the maximum value 246 to obtain the first value 242,and the first value 242 is less than the maximum value 246.

With reference back to FIG. 5, the throat dimension between 0% of thespan and 20% of the span of the adjacent ones of the plurality ofairfoils 204 has a second value 244. The second value 244 is less thanthe first value 242 and is less than the maximum value 246. In oneexample, the second value 244 is about 0.4 (40%) to about 0.7 (70%) ofthe maximum value 246 of the throat dimension distribution 240. Withreference to FIG. 7, a second throat dimension 282 is shown as definedbetween adjacent ones of the airfoils 204. FIG. 7 is a cross-sectionalview through two adjacent airfoils 204, taken along an arc length (inthe tangential direction or along the T-axis) of the rotor 200 startingfrom line 7-7 of FIG. 3 into the page. As shown in FIG. 7, the secondthroat dimension 282 of the throat dimension distribution 240 is definedas the minimum physical distance between the two airfoils 204 at aspanwise location between 0% of the span and 20% of the span, and in theexample of FIG. 7 the second throat dimension 282 is at about 5% span.The second throat dimension 282 is divided by the maximum value 246 toobtain the second value 244, and the second value 244 is less than 0.7(70%) of the maximum value 246 of the throat dimension distribution 240.In one example, the second value 244 is at about 5% span and is lessthan 0.6 (60%) of the maximum value 246 of the throat dimensiondistribution 240.

With reference back to FIG. 5, in this example, the throat dimension hasa maximum value 246 at a spanwise location between 60% of the span and90% of the span of the adjacent ones of the plurality of airfoils 204.The maximum value 246 is an absolute maximum value for the throatdimension distribution 240. In one example, the maximum value 246 islocated or defined at about 75% of the span. A dashed line 247 thatextends from the maximum value 246 to the horizontal axis 236 isprovided in FIG. 5 for ease of reference. The first value 242 is lessthan 70% of the maximum value 246. Line 249 that represents 70% of themaximum value 246 is provided in FIG. 5 for ease of reference. As themaximum value 246 is the largest value for the throat dimensiondistribution 240, the maximum value 246 of the normalized throatdimension is 1.0. With reference to FIG. 8, the maximum value 246 isshown as defined between adjacent ones of the airfoils 204. FIG. 8 is across-sectional view through two adjacent airfoils 204, taken along anarc length (in the tangential direction or along the T-axis) of therotor 200 starting from line 8-8 of FIG. 3 into the page. As shown inFIG. 8, the maximum value 246 of the throat dimension distribution 240is defined as the minimum physical distance between the two airfoils 204at a spanwise location between 60% of the span and 90% of the span, andin the example of FIG. 8, the maximum value 246 is at about 75% span.

With reference back to FIG. 5, the throat dimension has a third value248 at 10% of the span of the adjacent ones of the plurality of airfoils204 above the spanwise location (toward the tip 212 or 100% span) of themaximum value 246. The third value 248 of the throat dimension at 10% ofthe span of the adjacent ones of the plurality of airfoils 204 above thespanwise location of the maximum value 246 is less than 97% of themaximum value 246 or has a normalized throat value that is less than0.97. In other embodiments, the third value 248 of the throat dimensionat 10% of the span of the adjacent ones of the plurality of airfoils 204above the spanwise location of the maximum value 246 is less than 96% ofthe maximum value 246 or has a normalized throat value that is less than0.96. In the example of the maximum value 246 at 75% span, the thirdvalue 248 is at 85% span. With reference to FIG. 9, a third throatdimension 284 is shown as defined between adjacent ones of the airfoils204. FIG. 9 is a cross-sectional view through two adjacent airfoils 204,taken along an arc length (in the tangential direction or along theT-axis) of the rotor 200 starting from line 9-9 of FIG. 3 into the page.As shown in FIG. 9, the third throat dimension 284 of the throatdimension distribution 240 is defined as the minimum physical distancebetween the two airfoils 204 at a spanwise location at 10% span abovethe spanwise location of the maximum value 246, which in the example ofFIG. 9 the third throat dimension 284 is at about 85% span. The thirdthroat dimension 284 is divided by the maximum value 246 to obtain thethird value 248.

With reference back to FIG. 5, the throat dimension also has a fourthvalue 250 at 10% of the span of the adjacent ones of the airfoils 204below the spanwise location (toward the root 210 or 0% span) of themaximum value 246. The fourth value 250 of the throat dimension at 10%of the span of the adjacent ones of the airfoils 204 below the spanwiselocation of the maximum value 246 is less than 97% of the maximum value246 or has a normalized throat value that is less than 0.97. In otherembodiments, the fourth value 250 of the throat dimension at 10% of thespan of the adjacent ones of the plurality of airfoils 204 below thespanwise location of the maximum value 246 is less than 96% of themaximum value 246 or has a normalized throat value that is less than0.96. In the example of the maximum value 246 at 75% span, the fourthvalue 250 is at 65% span. With reference to FIG. 10, a fourth throatdimension 286 is shown as defined between adjacent ones of the airfoils204. FIG. 10 is a cross-sectional view through two adjacent airfoils204, taken along an arc length (in the tangential direction or along theT-axis) of the rotor 200 starting from line 10-10 of FIG. 3 into thepage. As shown in FIG. 10, the fourth throat dimension 286 of the throatdimension distribution 240 is defined as the minimum physical distancebetween the two airfoils 204 at a spanwise location at 10% span belowthe spanwise location of the maximum value 246, and in the example ofFIG. 10 the fourth throat dimension 286 is at about 65% span. The fourththroat dimension 286 is divided by the maximum value 246 to obtain thefourth value 250.

Thus, at 10% of the span of the adjacent ones of the airfoils 204 aboveor below the spanwise location of the maximum value 246, the throatdimension is less than 97% of the maximum value 246, as shown in FIG. 5.Stated another way, the value of the throat dimension at 10% of the spanof the adjacent ones of the airfoils 204 above or below the spanwiselocation of the maximum value 246 is reduced by at least 3% of themaximum value 246. Line 252 that represents 97% of the maximum value 246is provided in FIG. 5 for ease of reference.

In addition, the throat dimension has a fifth value 254 at 10% of thespan of the adjacent ones of the plurality of airfoils is less than 60%of the maximum value 246 of the throat dimension distribution 240 or hasa normalized throat value that is less than 0.6. Line 256 thatrepresents 60% of the maximum value 246 is provided in FIG. 5 for easeof reference.

With reference back to FIG. 5, the throat dimension between 40% of thespan and 60% of the span of the adjacent ones of the plurality ofairfoils 204 has a sixth value 262. The sixth value 262 is less than thethird value 248 and is less than the fourth value 250. In one example,the sixth value 262 is about 0.8 to about 0.9 of the maximum value 246of the throat dimension distribution 240. In this example, the sixthvalue 262 of the throat dimension distribution 240 is defined as theminimum physical distance between the two airfoils 204 at a spanwiselocation between 40% of the span and 60% of the span, which is dividedby the maximum value 246, and in this example, the sixth value 262 is ata spanwise location that is about 25% less than the spanwise location ofthe maximum value 246. As shown in FIG. 5, the sixth value 262 is about0.88 of the maximum value 246 of the throat dimension distribution 240and is at a spanwise location of about 50% span when the maximum value246 is at a spanwise location of about 75% span.

In this example, with reference to FIG. 5A, a graph shows the variationof a throat dimension distribution 240′ along the span S of the airfoils204. In FIG. 5A, the abscissa or horizontal axis 236′ is a normalizedvalue of the throat dimension, which is normalized by dividing thethroat dimension at the particular spanwise location by an averagethroat dimension between adjacent ones of the airfoils 204 along theentirety of the span of the airfoils 204 (and the normalized throatdimension may be multiplied by 100 to arrive at a percentage of theaverage value); and the ordinate or vertical axis 238 is the spanwiselocation or location along the span of the adjacent airfoils 204 (spanis 0% at the root 210 (FIG. 3) and span is 100% at the tip 212 (FIG.3)). In one example, the normalized value of the throat dimension rangesfrom about 0.6 to about 1.3. As used herein the “average throatdimension” is the average throat dimension between the airfoils 204taken along the span S of the airfoils 204 from 0% at the root 210 (FIG.3) to 100% at the tip 212 (FIG. 3).

As shown in FIG. 5A, the throat dimension between 90% of the span and100% of the span of the adjacent ones of the plurality of airfoils 204has a first value 242′. In one example, the first value 242′ is about0.7 (70%) to about 0.8 (80%) of the average throat dimension of thethroat dimension distribution 240′. The first value 242′ of the throatdimension distribution 240′ is defined as the minimum physical distancebetween the two airfoils 204 at a spanwise location between 90% of thespan and 100% of the span, and in this example, the first value 242′ isat the tip 212 or 100% span.

The throat dimension between 0% of the span and 20% of the span of theadjacent ones of the plurality of airfoils 204 has a second value 244′.The second value 244′ is less than the first value 242′. In one example,the second value 244′ is about 0.6 (60%) to about 0.7 (70%) of theaverage throat dimension of the throat dimension distribution 240′. Thesecond value 244′ of the throat dimension distribution 240′ is definedas the minimum physical distance between the two airfoils 204 at aspanwise location between 0% of the span and 20% of the span, and inthis example, the second value 244′ is at about 5% span and is less than0.7 (70%) of the average throat dimension of the throat dimensiondistribution 240′. The throat dimension distribution 240′ betweenadjacent ones of the airfoils 204 at 0% span (at the root 210 (FIG. 3))is a seventh value 260′ for the throat dimension, and the throatdimension changes from 0% span to the second value 244′. The seventhvalue 260′ is less than the first value 242′ and the second value 244′,and is an absolute minimum value for the throat dimension distribution240′.

With continued reference to FIG. 5A, the throat dimension has a maximumvalue 246′ at a spanwise location between 60% of the span and 90% of thespan of the adjacent ones of the plurality of airfoils 204. In oneexample, the maximum value 246′ is located or defined at about 75% ofthe span. The maximum value 246′ is the largest value for the throatdimension distribution 240′, and the maximum value 246′ is about 1.2(120%) to about 1.3 (130%) of the average throat dimension of the throatdimension distribution 240′. The maximum value 246′ of the throatdimension distribution 240′ is defined as the minimum physical distancebetween the two airfoils 204 at a spanwise location between 60% of thespan and 90% of the span, and in this example, the maximum value 246′ isat about 75% span.

The throat dimension has a third value 248′ at 10% of the span of theadjacent ones of the plurality of airfoils 204 above the spanwiselocation (toward the tip 212 or 100% span) of the maximum value 246′.The third value 248′ of the throat dimension at 10% of the span of theadjacent ones of the plurality of airfoils 204 above the spanwiselocation of the maximum value 246′ is less than 97% of the maximum value246′. In the example of the maximum value 246′ of about 1.25 (125%) ofthe average throat dimension of the throat dimension distribution 240′,the third value 248′ has a normalized throat value that is less thanabout 1.2. In the example of the maximum value 246′ at 75% span, thethird value 248′ is at 85% span. The third value 248′ of the throatdimension distribution 240′ is defined as the minimum physical distancebetween the two airfoils 204 at a spanwise location at 10% span abovethe spanwise location of the maximum value 246′, which in this example,is at about 85% span.

With continued reference to FIG. 5A, the throat dimension also has afourth value 250′ at 10% of the span of the adjacent ones of theairfoils 204 below the spanwise location (toward the root 210 or 0%span) of the maximum value 246′. The fourth value 250′ of the throatdimension at 10% of the span of the adjacent ones of the airfoils 204below the spanwise location of the maximum value 246′ is less than 97%of the maximum value 246′. In the example of the maximum value 246′ ofabout 1.25 (125%) of the average throat dimension of the throatdimension distribution 240′, the fourth value 250′ has a normalizedthroat value that is less than about 1.2. In the example of the maximumvalue 246′ at 75% span, the fourth value 250′ is at 65% span. The fourthvalue 250′ of the throat dimension distribution 240′ is defined as theminimum physical distance between the two airfoils 204 at a spanwiselocation at 10% span below the spanwise location of the maximum value246′, which in this example, is at about 65% span.

Thus, at 10% of the span of the adjacent ones of the airfoils 204 aboveor below the spanwise location of the maximum value 246′, the throatdimension is less than 97% of the maximum value 246′. Stated anotherway, the value of the throat dimension at 10% of the span of theadjacent ones of the airfoils 204 above or below the spanwise locationof the maximum value 246′ is reduced by at least 3% of the maximum value246′.

In addition, the throat dimension has a fifth value 254′ at 10% of thespan of the adjacent ones of the plurality of airfoils that is less than60% of the maximum value 246′ of the throat dimension distribution 240′.In the example of the maximum value 246′ of about 1.25 (125%) of theaverage throat dimension of the throat dimension distribution 240′, thefifth value 254′ has a normalized throat value that is less than about0.75.

With continued reference to FIG. 5A, the throat dimension between 40% ofthe span and 60% of the span of the adjacent ones of the plurality ofairfoils 204 has a sixth value 262′. The sixth value 262′ is less thanthe third value 248′ and is less than the fourth value 250′. In oneexample, the sixth value 262′ is about 1.0 to about 1.2 of the averagethroat dimension of the throat dimension distribution 240′. In thisexample, the sixth value 262′ of the throat dimension distribution 240′is defined as the minimum physical distance between the two airfoils 204at a spanwise location between 40% of the span and 60% of the span, andin this example the sixth value 262′ is at a spanwise location that isabout 25% less than the spanwise location of the maximum value 246. Asshown in FIG. 5A, is at a spanwise location of about 50% span when themaximum value 246′ is at a spanwise location of about 75% span.

With continued reference to FIG. 5A, by providing the throat dimensiondistribution 240′ with the maximum value 246′ of the throat dimensionbetween 60% span and 90% span with the third value 248′ and the fourthvalue 250′ at 10% of the span of the adjacent ones of the airfoils 204above or below the spanwise location of the maximum value 246′ at lessthan 97% of the maximum value 246′, the throat dimension distribution240′ provides increased flow capacity in contrast to a conventionalthroat dimension distribution 275. By providing the value of the throatdimension at 10% of the span of the adjacent ones of the airfoils 204above or below the spanwise location of the maximum value that is lessthan 97% of the maximum value, the throat dimension distribution 240′ ofthe present disclosure provides increased flow capacity whilemaintaining an efficiency and flutter margin of the rotor 200. In thisregard, by providing the value of the throat dimension at 10% of thespan of the adjacent ones of the airfoils 204 above or below thespanwise location of the maximum value that is less than 97% of themaximum value, the throat dimension is reduced at the tip but increasedbetween 60% and 90% of the span of the adjacent ones of the airfoils204, which reduces flutter risk while increasing flow capacity.

With the airfoils 204 formed, the airfoils 204 are coupled to the rotorhub 222 to form the rotor 200. As discussed, each of the airfoils 204are spaced apart about the circumference of the rotor disk 202 by thethroat dimension distribution 240. With reference to FIG. 5, the throatdimension distribution 240 between adjacent ones of the airfoils 204 at0% span (at the root 210 (FIG. 3)) is a seventh value 260 for the throatdimension, and the throat dimension changes from 0% span to the secondvalue 244. The seventh value 260 is less than the first value 242 andthe second value 244. The seventh value 260 is an absolute minimum valuefor the throat dimension in the throat dimension distribution 240. Thesecond value 244 is at a spanwise location between 0% and 10% of thespan. From the second value 244, the throat dimension changes to thesixth value 262, which is less than the fourth value 250. From the sixthvalue 262, the throat dimension changes to the fourth value 250, whichis less than 97% of the maximum value 246 and is located at a spanwiselocation that is 10% less than a spanwise location of the maximum value246. From the fourth value 250, the throat dimension changes to themaximum value 246. The maximum value 246 is at a spanwise locationbetween 60% and 90% of the span of the airfoils 204. From the maximumvalue 246, the throat dimension changes to the third value 248, which isless than 97% of the maximum value 246 and is located at a spanwiselocation that is 10% above a spanwise location of the maximum value 246.From the third value 248, the throat dimension changes to the firstvalue 242, which is at a spanwise location between 90% and 100% of thespan. The first value 242 and the second value 244 are each less than70% of the maximum value 246, and the second value 244 is less than 60%of the maximum value 246 and is less than the first value 242. The firstvalue 242 is greater than 60% of the maximum value 246.

Generally, in this example, the throat dimension distribution 240increases from 0% span to the second value 244, and increases to thesixth value 262. The throat dimension distribution 240 also generallyincreases from the sixth value 262 to the fourth value 250. From thefourth value 250, the throat dimension distribution 240 generallyincreases to the maximum value 246 and decreases to the third value 248.From the third value 248, the throat dimension distribution 240decreases to the first value 242. It should be noted that the increasesand decreases in the throat dimension distribution 240 may not bemonotonic as shown in FIG. 5. Rather, one or more of the changes inthroat dimension distribution 240 may include a local increase or alocal decrease before the throat dimension distribution 240 changesbetween the various values 244, 262, 250, 246, 248, 242.

With the rotor 200 formed, the rotor 200 is installed in the gas turbineengine 100 (FIG. 1). In general, the rotor 200 may be incorporated intoone or more of the engine sections described with regard to FIG. 1above. For example and additionally referring to FIG. 1, the rotor 200may be incorporated into the fan section 102 such that, as the rotor 200rotates, the airfoils 204 function to draw air into the gas turbineengine 100. Further, the rotor 200 may be incorporated into one or moreof the high pressure compressor 122 and/or the intermediate pressurecompressor 120 such that, as the rotor 200 rotates, the airfoils 204function to compress the air flowing through the airfoils 204.

Rotor Blade Camber Distribution

As discussed previously, with reference back to FIG. 2, the rotor 200may include the plurality of rotor blades 300, which have a total camberdistribution 302 that reduces flutter. In the example of the rotor 200,each of the rotor blades 300 may be referred to as an “airfoil 300.” Theairfoils 300 extend in a radial direction (relative to the longitudinalaxis 140 of the gas turbine engine 100) about the periphery of the rotordisk 202, and may be spaced apart by the throat dimension distribution240. With reference to FIG. 11, one of the airfoils 300 for use with therotor 200 of the gas turbine engine 100 is shown. The airfoils 300 eachinclude a leading edge 306, an axially-opposed trailing edge 308, a baseor root 310, and a radially-opposed tip 312. The tip 312 is spaced fromthe root 310 in a blade height, span or spanwise direction, whichgenerally corresponds to the radial axis (R-axis) of the coordinatelegend 211 in the view of FIG. 11. As shown in FIG. 11, the span S ofeach of the airfoils 300 is 0% at the root 310 (where the airfoil 300 iscoupled to the rotor hub 222) and is 100% at the tip 312. In thisexample, the airfoils 300 are arranged in a ring or annular arraysurrounded by the static fan shroud 216. The static fan shroud 216 is,in turn, circumscribed by the annular housing piece 218 defining thecontainment pocket 220. The airfoils 300 and the rotor disk 202 aregenerally composed of a metal, metal alloy or a polymer-based material,such as a polymer-based composite material. In one example, the airfoils300 are integrally formed with the rotor disk 202 as a monolithic orsingle piece structure commonly referred to as a bladed disk or “blisk.”In other examples, the airfoils 300 may be insert-type blades, which arereceived in mating slots provided around the outer periphery of rotordisk 202. In still further examples, the rotor 200 may have a differentconstruction. Generally, then, it should be understood that the rotor200 is provided by way of non-limiting example and that the rotor 200(and the airfoils 300 described herein) may be fabricated utilizingvarious different manufacturing approaches. Such approaches may include,but are not limited to, casting and machining, three dimensional metalprinting processes, direct metal laser sintering, Computer NumericalControl (CNC) milling of a preform or blank, investment casting,electron beam melting, binder jet printing and powder metallurgy, plylay-up, to list but a few examples. Regardless of its construction, therotor 200 includes the rotor hub 222 defining a hub flow path. The hubflow path extends over the outer surface of the rotor 200 and betweenthe airfoils 300 to guide airflow along from the inlet end (inducer orleading edge) to the outlet end (exducer or trailing edge) of the rotor200. As shown in FIG. 11, each of the plurality of airfoils 300 iscoupled to the rotor hub 222 at the root 310 (0% span). It should benoted that while each of the plurality of airfoils 300 are illustratedherein as being coupled to the rotor hub 222 at an angle relative to theaxial direction (A-axis), one or more of the plurality of airfoils 300may be coupled to the rotor hub 222 along a straight line. Further, itshould be noted that one or more of the plurality of airfoils 300 may becoupled to the rotor hub 222 along a complex curved surface. It shouldbe noted that in the instances where the plurality of airfoils 300 arecoupled to the rotor hub 222 at an angle, the span remains at 0% at theroot 310. In other words, the span of each of the plurality of airfoils300 remains at 0% at the root 310 regardless of the shape of the rotorhub 222.

With reference to FIG. 12, each of the airfoils 300 further includes afirst principal face or a “pressure side” 324 and a second, opposingface or a “suction side” 326. The pressure side 324 and the suction side326 extend in a chordwise direction along a chord line CH₁ and areopposed in a thickness direction normal to a mean camber line 328, whichis illustrated as a dashed line in FIG. 12 that extends from the leadingedge 306 to the trailing edge 308. The pressure side 324 and the suctionside 326 extend from the leading edge 306 to the trailing edge 308. Inone example, each of the airfoils 300 is somewhat asymmetrical and has atotal camber θ_(T) along the mean camber line 328. The pressure side 324has a contoured, generally concave surface geometry, which gently bendsor curves in three dimensions. The suction side 326 has a contoured,generally convex surface geometry, which likewise bends or curves inthree dimensions.

In one example, each of the airfoils 300 has an inlet metal angle β1defined at the leading edge 306. The inlet metal angle β1 is the anglebetween a reference line L1 that is tangent to the mean camber line 328at the leading edge 306 and a reference line L2 that is parallel to theengine center line or the longitudinal axis 140 of the gas turbineengine 100 (FIG. 2) and normal to the direction of rotation DR. Each ofthe airfoils 300 also have an exit metal angle β2 defined at thetrailing edge 308. The exit metal angle β2 is the angle between areference line L3 that is tangent to the mean camber line 328 at thetrailing edge 308 and a reference line L4 that is parallel to the enginecenter line or the longitudinal axis 140 of the gas turbine engine 100(FIG. 2) and normal to the direction of rotation DR. Generally, at aparticular span of the airfoil 300, the airfoils 300 have the inletmetal angle β1 and the exit metal angle β2. The inlet metal angle β1 andthe exit metal angle β2 for the airfoil 300 may vary over the span S ofthe airfoil 300 based on the total camber distribution 302 of theairfoil 300 (FIG. 11). As used herein, a total camber θ_(T) of theairfoil 300 at a particular span is defined by the following equation:θ_(T)=β₁−β₂  (1)

Wherein, θ_(T) is the total camber of the airfoil 300 at the particularspan; β1 is the inlet metal angle in degrees; and β2 is the exit metalangle in degrees. Thus, as used herein, the “total camber” of the meancamber line 328 of the airfoil 300 at a particular span is a differencebetween an inlet metal angle (β1) and an exit metal angle (β2) at theparticular spanwise location. As will be discussed, the total camberdistribution 302 of each of the airfoils 300 varies over the span S(FIG. 11) of the airfoil 300 to reduce flutter. In this regard, as willbe discussed, the total camber distribution 302 of each of the airfoils300 has a reduced total camber θ_(T) at the root 310, which reduces thetwist-to-flex ratio of the fundamental vibratory mode shape associatedwith each of the airfoils 300. By reducing the twist-to-flex ratio ofthe fundamental vibratory mode shape through the change in the modeshape of each of the airfoils 300 that is obtained by providing areduced total camber θ_(T) at or near the root 310, each of the airfoils300 is less susceptible to flutter. For any section of an airfoil, thetwist-to-flex ratio is the amount of torsional rotation of the sectionrelative to the amount of translational displacement of the section fromthe mode of vibration.

In one example, with reference to FIG. 13, a graph shows the variationof the total camber distribution 302 along the span S of each of theairfoils 300. In FIG. 13, the abscissa or horizontal axis 336 is thetotal camber θ_(T) in degrees; and the ordinate or vertical axis 338 isthe spanwise location or location along the span S of each of theairfoils 300 (span is 0% at the root 310 (FIG. 11) and span is 100% atthe tip 312 (FIG. 11)).

As shown in FIG. 13, the total camber θ_(T) between 0% of the span and5% of the span of each of the airfoils 300 has a first value 340. In oneexample, the first value 340 of the total camber θ_(T) is about 34degrees to about 40 degrees, and in this example, is about 37 degrees.With reference to FIG. 14, the first value 340 of the total camber θ_(T)for each of the airfoils 300 is shown. FIG. 14 is a cross-sectional viewthrough one of the airfoils 300, taken from line 14-14 of FIG. 11 intothe page. As shown in FIG. 14, the first value 340 of the total camberθ_(T) is defined as the difference between an inlet metal angle β1A andan exit metal angle β2A at a spanwise location between 0% of the spanand 5% of the span, which in the example of FIG. 13 is at 0% span or atthe root 310. Thus, the first value 340 of the total camber θ_(T) at ornear the root 310 (between 0% span and 5% span of each of the airfoils300) is less than the maximum total camber value 342 of the total camberdistribution 302 of each of the airfoils 300. Stated another way, eachof the airfoils 300 has a locally reduced total camber θ_(T) at or nearthe root 310, which reduces the twist-to-flex ratio of the fundamentalvibratory mode shape associated with each of the airfoils 300.

With reference back to FIG. 13, the total camber θ_(T) between 5% of thespan and 20% of the span of each of the airfoils 300 has a maximum valueof total camber θ_(T) or maximum total camber value 342. In one example,the maximum total camber value 342 of the total camber θ_(T) is about 40degrees to about 45 degrees, and in this example, is about 42 degrees.With reference to FIG. 15, the maximum total camber value 342 of thetotal camber θ_(T) for each of the airfoils 300 is shown. FIG. 15 is across-sectional view through one of the airfoils 300, taken from line15-15 of FIG. 11 into the page. As shown in FIG. 15, the maximum totalcamber value 342 of the total camber θ_(T) is defined as the differencebetween an inlet metal angle β1B and an exit metal angle β2B at aspanwise location between 5% of the span and 20% of the span, which inthe example of FIG. 15 is at 12% span. The maximum total camber value342 is greater than the first value 340. Thus, in this example, thetotal camber θ_(T) of each of the airfoils 300 increases from the root310 (FIG. 11) to the maximum total camber value 342.

With reference back to FIG. 13, the total camber θ_(T) between 20% ofthe span and 30% of the span of each of the airfoils 300 has a secondvalue 344. In one example, the second value 344 of the total camberθ_(T) is about 32 degrees to about 38 degrees, and in this example, isabout 35 degrees. With reference to FIG. 16, the second value 344 of thetotal camber θ_(T) for each of the airfoils 300 is shown. FIG. 16 is across-sectional view through one of the airfoils 300, taken from line16-16 of FIG. 11 into the page. As shown in FIG. 16, the second value344 of the total camber θ_(T) is defined as the difference between aninlet metal angle β1C and an exit metal angle β2C at a spanwise locationbetween 20% of the span and 30% of the span, which in the example ofFIG. 16 is at 25% span. The second value 344 is less than the maximumtotal camber value 342 and the second value 344 is less than the firstvalue 340. With reference back to FIG. 13, the total camber between 20%of the span and 30% of the span of each of the airfoils 300 has a fourthvalue 345. In one example, the fourth value 345 of the total camberθ_(T) is about 35 degrees to about 40 degrees, and in this example, isabout 39 degrees. The fourth value 345 of the total camber θ_(T) isdefined as the difference between an inlet metal angle β1C and an exitmetal angle β2C at a spanwise location between 20% of the span and 30%of the span, which in this example is at 20% span. Thus, in thisexample, the total camber θ_(T) of each of the airfoils 300 decreasesfrom the maximum total camber value 342 (FIG. 11) to the second value344.

With reference to FIG. 17, a portion of the total camber distribution302 of one of the airfoils 300 is shown. FIG. 17 is an overlay of thecross-sectional views of FIGS. 14-16 of the one of the airfoils 300. Asshown in FIG. 17, the total camber θ_(T) of each of the airfoils 300increases from the root 310 to the maximum total camber value 342, anddecreases from the maximum total camber value 342 to the second value344. In this example, with reference to FIG. 13, the total camber θ_(T)decreases monotonically from the second value 344 to the tip 312 (FIG.11) or decreases monotonically to a third value 346 at 100% of the span.The third value 346 is less than 20 degrees, and in one example, thethird value 346 of the total camber θ_(T) is about 3 degrees to about 10degrees, and in this example, is about 8 degrees.

Generally, in this example, the total camber θ_(T) of each of theairfoils 300 increases from 0% span to the maximum total camber value342, decreases from the maximum total camber value 342 to the secondvalue 344 and decreases from the second value 344 to the third value 346at 100% of the span. It should be noted that the increases and decreasesin the total camber θ_(T) of one or more of the airfoils 300 may not bemonotonic as shown in FIG. 13. Rather, one or more of the changes intotal camber θ_(T) may include a local increase or a local decreasebefore the total camber θ_(T) changes between the various values 342,344, 346.

It will be understood that the total camber distribution 302 of theairfoils 300 described with regard to FIGS. 11-17 may be configureddifferently to reduce flutter. In one example, with reference back toFIG. 13, the graph also shows an exemplary total camber distribution 402along the span S of each of the airfoils 300. In this example, the totalcamber θ_(T) between 0% of the span and 5% of the span of each of theairfoils 300 has a first value 440. In one example, the first value 440of the total camber θ_(T) is about 35 degrees to about 40 degrees, andin this example, is about 39 degrees at 0% span. The total camber θ_(T)of the total camber distribution 402 between 5% of the span and 20% ofthe span of each of the airfoils 300 has a maximum value of total camberor maximum total camber value 442. In one example, the maximum totalcamber value 442 of the total camber θ_(T) is about 42 degrees to about48 degrees, and in this example, is about 45 degrees at 12% span. Themaximum total camber value 442 is greater than the first value 440.Thus, for the total camber distribution 402, the total camber θ_(T) ofeach of the airfoils 300 increases from the root 310 (FIG. 11) to themaximum total camber value 442.

For the total camber distribution 402, the total camber θ_(T) between20% of the span and 30% of the span of each of the airfoils 300 has asecond value 444. In one example, the second value 444 of the totalcamber θ_(T) is about 38 degrees to about 42 degrees, and in thisexample, is about 40 degrees at 20% span. The second value 444 is lessthan the maximum total camber value 442 and the second value 444 is lessthan the first value 440. Thus, for the total camber distribution 402,the total camber θ_(T) of each of the airfoils 300 decreases from themaximum total camber value 442 to the second value 444.

For the total camber distribution 402, the total camber θ_(T) decreasesfrom the second value 444 to a third value 446 between 80% of the spanand 90% of the span of each of the airfoils 300. In one example, thethird value 446 of the total camber θ_(T) is about 8 degrees to about 12degrees, and in this example, is about 10 degrees at 85% span. The thirdvalue 446 is less than the maximum total camber value 442, the secondvalue 444 and the first value 440. In addition, for the total camberdistribution 402, the total camber θ_(T) increases from the third value446 to a fourth value 448 between 90% of the span and 100% of the spanof each of the airfoils 300. In one example, the fourth value 448 of thetotal camber θ_(T) is about 14 degrees to about 19 degrees, and in thisexample, is about 15 degrees at 100% span. The fourth value 448 isgreater than the third value 446, but the fourth value 448 is less thanthe maximum total camber value 442, the second value 444 and the firstvalue 440. The fourth value 448 of the total camber θ_(T) is less than20 degrees. Thus, for the total camber distribution 402, the totalcamber θ_(T) of each of the airfoils 300 decreases from the maximumtotal camber value 442 to the third value 446 between 80% and 90% span,and increases from the third value 446 to the tip 312 (FIG. 11) or 100%span. Thus, the total camber distribution 402 has a local increase nearthe tip 312 of each of the airfoils 300.

Generally, in the example of the total camber distribution 402, thetotal camber θ_(T) of each of the airfoils 300 increases from 0% span tothe maximum total camber value 442, decreases from the maximum totalcamber value 442 to the second value 444, decreases from the secondvalue 444 to the third value 446 and increases from the third value 446to the fourth value 448 at 100% of the span. It should be noted that theincreases and decreases in the total camber θ_(T) of the total camberdistribution 402 of one or more of the airfoils 300 may not be as shownin FIG. 13. Rather, one or more of the changes in total camber θ_(T) mayinclude a local increase or a local decrease before the total camberθ_(T) changes between the various values 444, 446, 448.

With continued reference to FIG. 13, by providing the total camberdistributions 302, 402 with the maximum total camber value 342, 442between 5% span and 20% span in contrast to conventional total camberdistributions 450, 452, the total camber distributions 302, 402 reducethe twist-to-flex ratio of the fundamental vibratory mode shapeassociated with each of the airfoils 300. By providing the maximum totalcamber value 342, 442 at a spanwise location away from the root 310 or0% span, the total camber distributions 302, 402 of the presentdisclosure each reduce flutter associated with the airfoil 300 bydecreasing the total camber θ_(T) of the rotor blade 300 near and at theroot 310 or 0% span of the rotor blade 300, which changes thetwist-to-flex ratio of each of the rotor blades 300.

With each of the airfoils 300 formed with the total camber distribution302 or the total camber distribution 402, the airfoils 300 are coupledto the rotor hub 222 to form the rotor 200. With the rotor 200 formed,the rotor 200 is installed in the gas turbine engine 100 (FIG. 1). Ingeneral, the rotor 200 may be incorporated into one or more of theengine sections described with regard to FIG. 1 above. For example andadditionally referring to FIG. 1, the rotor 200 may be incorporated intothe fan section 102 such that, as the rotor 200 rotates, the airfoils300 function to draw air into the gas turbine engine 100 with reducedsusceptibility to flutter. Further, the rotor 200 may be incorporatedinto one or more of the high pressure compressor 122 and/or theintermediate pressure compressor 120 such that, as the rotor 200rotates, the airfoils 300 function to compress the air flowing throughthe airfoils 300 with reduced susceptibility to flutter.

It will be understood that the total camber distribution 302, 402 of theairfoils 300 described with regard to FIGS. 11-17 may be configureddifferently to reduce flutter. In one example, with reference to FIG.18, a rotor 450 is shown for use with the gas turbine engine 100. Therotor 450 includes a rotor disk 452 from which the plurality of airfoils300 extends. In one embodiment, the airfoils 300 are integrally formedwith the rotor disk 452 as a monolithic or single piece structurecommonly referred to as a bladed disk or “blisk.” In other embodiments,the airfoils 300 may be insert-type blades, which are received in matingslots provided around the outer periphery of rotor disk 452. Regardlessof its construction, the rotor 450 includes a rotor hub 454 defining ahub flow path. The hub flow path extends over the outer surface of therotor 450 and between the airfoils 300 to guide airflow along from theinlet end (inducer or leading edge) to the outlet end (exducer ortrailing edge) of the rotor 450. In this example, the rotor hub 454extends at a hub angle θ2, which is formed between the longitudinal axis140 of the gas turbine engine 100 and line extending from referencepoint P1 to reference point P2. In this example, the hub angle θ2defines a hub slope angle for the rotor disk 452 and is greater than 20degrees. Typically, a hub angle for a rotor is less than about 20degrees. In certain instances, it is desirable to have a high rotor hubpressure rise, which is enabled by this higher value for the hub angleθ2, but this higher value may impact mode shape. By integrally formingthe airfoils 300 having the total camber distribution 302, 402 with therotor 450 having the hub slope angle or hub angle θ2, the rotor 450having the increased hub slope angle (hub angle θ2 greater than about 20degrees) provides for high hub pressure rise with reduced likelihood offlutter.

Rotor Blade Location of Local Maximum Thickness Distribution

As discussed previously, with reference back to FIG. 2, the rotor 200may include the plurality of rotor blades 500, which have a location oflocal maximum thickness distribution 502 that provides robustness toforeign objects without increasing a weight of the rotor blade 500. Inthe example of the rotor 200, each of the rotor blades 500 may bereferred to as an “airfoil 500.” The airfoils 500 extend in a radialdirection (relative to the longitudinal axis 140 of the gas turbineengine 100) about the periphery of the rotor disk 202, and may be spacedapart by the throat dimension distribution 240. With reference to FIG.19, one of the airfoils 500 for use with the rotor 200 of the gasturbine engine 100 is shown. The airfoils 500 each include a leadingedge 506, an axially-opposed trailing edge 508, a base or root 510, anda radially-opposed tip 512. The tip 512 is spaced from the root 510 in ablade height, span or spanwise direction, which generally corresponds tothe radial axis (R-axis) of the coordinate legend 211 in the view ofFIG. 19. As shown in FIG. 19, the span S of each of the airfoils 500 is0% at the root 510 (where the airfoil 500 is coupled to the rotor hub222) and is 100% at the tip 512. In this example, the airfoils 500 arearranged in a ring or annular array surrounded by the static fan shroud216. The static fan shroud 216 is, in turn, circumscribed by the annularhousing piece 218 defining the containment pocket 220. The airfoils 500and the rotor disk 202 are generally composed of a metal, metal alloy ora polymer-based material, such as a polymer-based composite material. Inone example, the airfoils 500 are integrally formed with the rotor disk202 as a monolithic or single piece structure commonly referred to as abladed disk or “blisk.” In other examples, the airfoils 500 may beinsert-type blades, which are received in mating slots provided aroundthe outer periphery of rotor disk 202. In still further examples, therotor 200 may have a different construction. Generally, then, it shouldbe understood that the rotor 200 is provided by way of non-limitingexample and that the rotor 200 (and the airfoils 500 described herein)may be fabricated utilizing various different manufacturing approaches.Such approaches may include, but are not limited to, casting andmachining, three dimensional metal printing processes, direct metallaser sintering, Computer Numerical Control (CNC) milling of a preformor blank, investment casting, electron beam melting, binder jetprinting, powder metallurgy and ply lay-up, to list but a few examples.Regardless of its construction, the rotor 200 includes the rotor hub 222defining a hub flow path. The hub flow path extends over the outersurface of the rotor 200 and between the airfoils 500 to guide airflowalong from the inlet end (inducer or leading edge) to the outlet end(exducer or trailing edge) of the rotor 200. As shown in FIG. 19, eachof the plurality of airfoils 500 is coupled to the rotor hub 222 at theroot 510 (0% span). It should be noted that while each of the pluralityof airfoils 500 are illustrated herein as being coupled to the rotor hub222 at an angle relative to the axial direction (A-axis), one or more ofthe plurality of airfoils 500 may be coupled to the rotor hub 222 alonga straight line. Further, it should be noted that one or more of theplurality of airfoils 500 may be coupled to the rotor hub 222 along acomplex curved surface. It should be noted that in the instances wherethe plurality of airfoils 500 are coupled to the rotor hub 222 at anangle, the span remains at 0% at the root 510. In other words, the spanof each of the plurality of airfoils 500 remains at 0% at the root 510regardless of the shape of the rotor hub 222.

With reference to FIG. 20, each of the airfoils 500 further includes afirst principal face or a “pressure side” 524 and a second, opposingface or a “suction side” 526. The pressure side 524 and the suction side526 extend in a chordwise direction along a chord line CH₂ and areopposed in a thickness direction normal to a mean camber line 528, andthe mean camber line 528 is illustrated as a dashed line in FIG. 20 thatextends from the leading edge 506 to the trailing edge 508. The pressureside 524 and the suction side 526 extend from the leading edge 506 tothe trailing edge 508. In one example, each of the airfoils 500 issomewhat asymmetrical and may be cambered along the mean camber line528, for example, each of the airfoils 500 may include the total camberdistribution 302, 402. The pressure side 524 has a contoured, generallyconcave surface geometry, which gently bends or curves in threedimensions. The suction side 526 has a contoured, generally convexsurface geometry, which likewise bends or curves in three dimensions. Inother embodiments, the airfoils 500 may not be cambered and may beeither symmetrical or asymmetrical.

In one example, at each spanwise location along the span S of each ofthe airfoils 500, each of the airfoils 500 has a total length or totalarc distance S_(Total) defined from the leading edge 506 to the trailingedge 508 along the mean camber line 528. In addition, at each spanwiselocation along the span S of each of the airfoils 500, each of theairfoils 500 has a first length or first arc distance S_(Arc), which isdefined as the arc distance along the mean camber line 528 from theleading edge 506 to a position 530 of local maximum thickness MT for theparticular span S. Stated another way, for each spanwise location alongthe span S of the airfoils 500, the airfoil 500 has a position 530 orlocation of local maximum thickness LMT, which is defined as a ratio ofthe first arc distance S_(Arc) along the mean camber line 528 associatedwith the respective spanwise location between the leading edge 506 andthe location of the local maximum thickness LMT to the total arcdistance S_(Total) along the respective mean camber line 528 from theleading edge 506 to the trailing edge 508, or:

$\begin{matrix}{{LMT} = \frac{S_{Arc}}{S_{Total}}} & (2)\end{matrix}$

Wherein, LMT is the location of local maximum thickness for theparticular spanwise location of the airfoil 500; S_(Arc) is the firstarc distance defined along the mean camber line 528 between the leadingedge 506 and the position 530 (FIG. 20) of the local maximum thicknessMT for the particular spanwise location of the airfoil 500; andS_(Total) is total arc distance along the mean camber line 528 from theleading edge 506 to the trailing edge 508 for the particular spanwiselocation of the airfoil 500. The local maximum thickness MT is thegreatest distance between the pressure side 524 and the suction side 526that is normal to the mean camber line 528 for the particular spanwiselocation. In this example, as will be discussed, the location of localmaximum thickness (LMT) distribution 502 varies over the span S of theairfoils 500 to provide robustness to foreign object encounters withoutincreasing a weight of the rotor blade 500, reducing flow capacity orimpacting efficiency.

In one example, with reference to FIG. 21, a graph shows the location oflocal maximum thickness (LMT) distribution 502 along the span S of eachof the airfoils 500. In FIG. 21, the abscissa or horizontal axis 536 isthe location of the local maximum thickness or LMT; and the ordinate orvertical axis 538 is the spanwise location or location along the span Sof each of the airfoils 500 (span is 0% at the root 510 (FIG. 19) andspan is 100% at the tip 512 (FIG. 19)).

As shown in FIG. 21, the location of the local maximum thickness or LMTbetween 0% of the span and 10% of the span of each of the airfoils 500increases from a position value 539 at the root or 0% span to a firstposition value 540. In one example, the position value 539 is about 0.35to about 0.40, and in this example, the position value 539 is about 0.39at 0% span. The first position value 540 of the location of the localmaximum thickness or LMT is about 0.42 to about 0.47, and in thisexample, is about 0.45 at about 10% span of the airfoil 500. Withreference to FIG. 22, the first position value 540 of the location ofthe local maximum thickness or LMT for each of the airfoils 500 isshown. FIG. 22 is a cross-sectional view through one of the airfoils500, taken from line 22-22 of FIG. 19 into the page. As shown in FIG.22, the first position value 540 of the location of the local maximumthickness or LMT is defined as the ratio between the first arc distanceS_(Arc-A) defined along the mean camber line 528 between the leadingedge 506 and the position of the local maximum thickness MT_(A) for theairfoil 500 between 0% of the span and 10% of the span; and S_(Total-A)is total arc distance along the mean camber line 528 from the leadingedge 506 to the trailing edge 508 for the airfoil 500 between 0% of thespan and 10% of the span. In this example, the position value of thelocation of the local maximum thickness or LMT increases from the rootor 0% span to the first position value 540, which is at 10% span.

With reference back to FIG. 21, the location of the local maximumthickness or LMT between 20% of the span and 50% of the span of each ofthe airfoils 500 has a second position value 542. In one example, thesecond position value 542 of the location of the local maximum thicknessor LMT is about 0.50 to about 0.55, and in this example, is about 0.53at about 30% span of the airfoil 500. With reference to FIG. 23, thesecond position value 542 of the location of the local maximum thicknessor LMT for each of the airfoils 500 is shown. FIG. 23 is across-sectional view through one of the airfoils 500, taken from line23-23 of FIG. 19 into the page. As shown in FIG. 23, the second positionvalue 542 of the location of the local maximum thickness or LMT isdefined as the ratio between the first arc distance S_(Arc-B) definedalong the mean camber line 528 between the leading edge 506 and theposition of the local maximum thickness MT_(B) for the airfoil 500between 20% of the span and 50% of the span; and S_(Total-B) is totalarc distance along the mean camber line 528 from the leading edge 506 tothe trailing edge 508 for the airfoil 500 between 20% of the span and50% of the span. Thus, in this example, from the first position value540 of the location of the local maximum thickness or LMT, the positionvalue of the location of the local maximum thickness or LMT increases tothe second position value 542 at about 30% span.

With reference back to FIG. 21, the location of the local maximumthickness or LMT between 60% of the span and 90% of the span of each ofthe airfoils 500 has a third position value 544. In one example, thethird position value 544 of the location of the local maximum thicknessor LMT is about 0.48 to about 0.52, and in this example, is about 0.51at about 70% span of the airfoil 500. With reference to FIG. 24, thethird position value 544 of the location of the local maximum thicknessor LMT for each of the airfoils 500 is shown. FIG. 24 is across-sectional view through one of the airfoils 500, taken from line24-24 of FIG. 19 into the page. As shown in FIG. 24, the third positionvalue 544 of the location of the local maximum thickness or LMT isdefined as the ratio between the first arc distance S_(Arc-C) definedalong the mean camber line 528 between the leading edge 506 and theposition of the local maximum thickness MT_(C) for the airfoil 500between 60% of the span and 90% of the span; and S_(Total-C) is totalarc distance along the mean camber line 528 from the leading edge 506 tothe trailing edge 508 for the airfoil 500 between 60% of the span and90% of the span. In this example, from the second position value 542 ofthe location of the local maximum thickness or LMT, the position valueof the location of the local maximum thickness or LMT decreases to thethird position value 544 at about 70% span.

With reference back to FIG. 21, the location of the local maximumthickness or LMT between 90% of the span and 100% of the span or the tip512 (FIG. 19) of each of the airfoils 500 has a fourth position value546. In one example, the fourth position value 546 of the location ofthe local maximum thickness or LMT is about 0.55 to about 0.60, and inthis example, is about 0.58 at about 100% span of the airfoil 500. Withreference to FIG. 25, the fourth position value 546 of the location ofthe local maximum thickness or LMT for each of the airfoils 500 isshown. FIG. 25 is a cross-sectional view through one of the airfoils500, taken from line 25-25 of FIG. 19 into the page. As shown in FIG.25, the fourth position value 546 of the location of the local maximumthickness or LMT is defined as the ratio between the first arc distanceS_(Arc-D) defined along the mean camber line 528 between the leadingedge 506 and the position of the local maximum thickness MT_(D) for theairfoil 500 between 90% of the span and 100% of the span; andS_(Total-D) is total arc distance along the mean camber line 528 fromthe leading edge 506 to the trailing edge 508 for the airfoil 500between 90% of the span and 100% of the span. In this example, from thethird position value 544 of the location of the local maximum thicknessor LMT, the position value of the location of the local maximumthickness or LMT increases to the fourth position value 546 at about100% span or the tip 512 (FIG. 19).

With reference to FIG. 26, a portion of the location of local maximumthickness distribution 502 of one of the airfoils 500 is shown. FIG. 26is an overlay of the cross-sectional views of FIGS. 22 and 23. As shownin FIG. 26, the location of local maximum thickness distribution 502 ofeach of the airfoils 500 increases from the first position value 540 at10% span to the second position value 542 at 30% span. Thus, the firstposition value 540 is a first minimum value, and the location of localmaximum thickness distribution 502 increases from the first minimumvalue to the second position value 542, which is a first maximum value.The first position value 540 is greater than the position value 539 atthe root (0% span), which is an absolute minimum value.

With reference to FIG. 27, a portion of the location of local maximumthickness distribution 502 of one of the airfoils 500 is shown. FIG. 27is an overlay of the cross-sectional views of FIGS. 23 and 24. As shownin FIG. 27, the location of local maximum thickness distribution 502 ofeach of the airfoils 500 decreases from the second position value 542 at30% span to the third position value 544 at 70% span. Thus, the thirdposition value 544 is a second minimum value, and the location of localmaximum thickness distribution 502 decreases from the second positionvalue 542 or the first maximum value at 30% span to the third positionvalue 544.

With reference to FIG. 28, a portion of the location of local maximumthickness distribution 502 of one of the airfoils 500 is shown. FIG. 28is an overlay of the cross-sectional views of FIGS. 24 and 25. As shownin FIG. 28, the location of local maximum thickness distribution 502 ofeach of the airfoils 500 increases from the third position value 544 at70% span to the fourth position value 546 at 100% span. Thus, the fourthposition value 546 is a second maximum value, and the location of localmaximum thickness distribution 502 increases from the third positionvalue 544 or the second minimum value at 70% span to the fourth positionvalue 546. The fourth position value 546 is an absolute maximum valuefor the location of local maximum thickness or LMT.

With reference back to FIG. 21, the location of local maximum thicknessdistribution 502 has the position value 539 at 0% span (at the root 210(FIG. 19)), and the value of the ratio (location of local maximumthickness or LMT) changes from 0% span to the first position value 540.The position value 539 is less than the first position value 540, and isthe smallest or the absolute minimum position value for the location oflocal maximum thickness or LMT over the span S of the airfoil 500. Thefirst position value 540 is at a spanwise location between 0% and 10% ofthe span, and in one example, is at 10% span. From the first positionvalue 540, the value of the ratio (location of local maximum thicknessor LMT) changes to the second position value 542, which is greater thanthe first position value 540 and the position value 539. The secondposition value 542 is at a spanwise location between 20% and 50% of thespan, and in one example, is at 30% span. From the second position value542, the value of the ratio (location of local maximum thickness or LMT)changes to the third position value 544, which is less than the secondposition value 542, but is greater than the first position value 540 andthe position value 539. The third position value 544 is at a spanwiselocation between 60% and 90% of the span, and in one example, is at 70%span. From the third position value 544, value of the ratio (location oflocal maximum thickness or LMT) changes to the fourth position value546, which is greater than the third position value 544, the secondposition value 542, the first position value 540 and the position value539. The fourth position value 546 is at a spanwise location between 90%and 100% of the span, and in one example, is at 100% span. The fourthposition value 546 is the absolute maximum position value for thelocation of local maximum thickness or LMT over the span S of theairfoil 500.

Generally, in this example, the location of local maximum thicknessdistribution 502 increases from 0% span to the first position value 540,and increases to the second position value 542. The location of localmaximum thickness distribution 502 also decreases from the secondposition value 542 to the third position value 544. From the thirdposition value 544, the location of local maximum thickness distribution502 generally increases to the fourth position value 546. Stated anotherway, the value of the ratio that defines the location of local maximumthickness or LMT increases from the root to the second position value542, decreases from the second position value 542 to the third positionvalue 544 and increases to the fourth position value 546.

It will be understood that the location of local maximum thicknessdistribution 502 of the airfoils 500 described with regard to FIGS.19-28 may be configured differently to provide robustness. In oneexample, with reference back to FIG. 21, the graph shows an exemplarylocation of local maximum thickness distribution 602 along the span S ofeach of the airfoils 500. For the location of local maximum thicknessdistribution 602, the location of the local maximum thickness or LMTbetween 0% of the span and 10% of the span of each of the airfoils 500increases from a position value 639 at the root or 0% span to a firstposition value 640. In one example, the position value 639 is about 0.30to about 0.35, and in this example, the position value 639 is about 0.34at 0% span. The first position value 640 of the location of the localmaximum thickness or LMT is about 0.40 to about 0.45, and in thisexample, is about 0.42 at about 10% span of the airfoil 500. Thus, thevalue of the location of the local maximum thickness or LMT increasesfrom the root or 0% span to the first position value 640, which is at10% span.

With continued reference to FIG. 21, for the location of local maximumthickness distribution 602, the location of the local maximum thicknessor LMT between 20% of the span and 50% of the span of each of theairfoils 500 has a second position value 642. In one example, the secondposition value 642 of the location of the local maximum thickness or LMTis about 0.48 to about 0.54, and in this example, is about 0.51 at about30% span of the airfoil 500. Thus, from the first position value 640 ofthe location of the local maximum thickness or LMT, the position valueof the location of the local maximum thickness or LMT increases to thesecond position value 642 at about 30% span.

For the location of local maximum thickness distribution 602, thelocation of the local maximum thickness or LMT between 60% of the spanand 90% of the span of each of the airfoils 500 has a third positionvalue 644. In one example, the third position value 644 of the locationof the local maximum thickness or LMT is about 0.35 to about 0.40, andin this example, is about 0.38 at about 85% span of the airfoil 500. Inthis example, from the second position value 642 of the location of thelocal maximum thickness or LMT, the position value of the location ofthe local maximum thickness or LMT decreases to the third position value644 at about 85% span.

For the location of local maximum thickness distribution 602, thelocation of the local maximum thickness or LMT between 90% of the spanand 100% of the span or the tip 512 (FIG. 19) of each of the airfoils500 has a fourth position value 646. In one example, the fourth positionvalue 646 of the location of the local maximum thickness or LMT is about0.38 to about 0.44, and in this example, is about 0.41 at about 100%span of the airfoil 500. In this example, from the third position value644 of the location of the local maximum thickness or LMT, a value ofthe location of the local maximum thickness or LMT increases to thefourth position value 646 at about 100% span or the tip 512 (FIG. 19).

Thus, the location of local maximum thickness distribution 602 has theposition value 639 at 0% span (at the root 510 (FIG. 19)), and value ofthe ratio (location of local maximum thickness or LMT) changes from 0%span to the first position value 640. The position value 639 is lessthan the first position value 640, and is the smallest or an absoluteminimum position value for the location of local maximum thickness orLMT over the span S of the airfoil 500 for the location of local maximumthickness distribution 602. The first position value 640 is at aspanwise location between 0% and 10% of the span, and in one example, isat 10% span. From the first position value 640, the value of the ratio(location of local maximum thickness or LMT) changes to the secondposition value 642, which is greater than the first position value 640and the position value 639. The second position value 642 is at aspanwise location between 20% and 50% of the span, and in one example,is at 30% span. From the second position value 642, the value of theratio (location of local maximum thickness or LMT) changes to the thirdposition value 644, which is less than the second position value 642,but is greater than the position value 639. The third position value 644is at a spanwise location between 60% and 90% of the span, and in oneexample, is at 85% span. From the third position value 644, the value ofthe ratio (location of local maximum thickness or LMT) changes to thefourth position value 646, which is greater than the third positionvalue 644. The fourth position value 646 is less than the secondposition value 642 and the first position value 640. The fourth positionvalue 646 is greater than the position value 639. The fourth positionvalue 646 is at a spanwise location between 90% and 100% of the span,and in one example, is at 100% span. In this example, the secondposition value 642 is an absolute maximum position value for the valueof the ratio (location of local maximum thickness or LMT) over the spanS of the airfoil 500 for the location of local maximum thicknessdistribution 602.

Generally, in this example, the location of local maximum thicknessdistribution 602 increases from 0% span to the first position value 640,and increases to the second position value 642. The location of localmaximum thickness distribution 602 also decreases from the secondposition value 642 to the third position value 644. From the thirdposition value 644, the location of local maximum thickness distribution602 generally increases to the fourth position value 646. Stated anotherway, the value of the ratio that defines the location of local maximumthickness or LMT increases from the root to the second position value642, decreases from the second position value 642 to the third positionvalue 644 and increases to the fourth position value 646.

It should be noted that the increases and decreases in the location oflocal maximum thickness or LMT of the location of local maximumthickness distribution 502 or the location of local maximum thicknessdistribution 602 of one or more of the airfoils 500 may not be as shownin FIG. 21. Rather, one or more of the changes in the location of thelocal maximum thickness or LMT may include a local increase or a localdecrease before the location of the local maximum thickness or LMTchanges between the various position values 539, 540, 542, 544, 546;639, 640, 642, 644, 646.

With continued reference to FIG. 21, by providing the location of localmaximum thickness distribution 502, 602 with the value of the ratio(location of local maximum thickness LMT) that increases from the rootto a position value 542, 642, decreases from the position value 542, 642to a position value 544, 644 and increases from the position value 544,644 to the position value 546, 646 at the tip or 100% span and theposition value 542, 642 is at a spanwise location within 20% to 50% ofthe span in contrast to conventional location of maximum thicknessdistributions 662, 664 and 668, the airfoil 500 has material positionedwhere it may reduce permanent deformation due to foreign objectencounters, without increasing the weight of the airfoil 500 or reducingflow capacity or efficiency of the rotor 200. By providing the locationof local maximum thickness distribution 502, 602 that each decrease fromthe position value 542, 642 at a spanwise location within 20% to 50% ofthe span and then increase to the tip or 100% span, the airfoil 500 hasimproved robustness without increasing a weight of the airfoil 500. Byproviding the position value 542, 642 at a spanwise location within 20%to 50% of the span, the location of local maximum thicknessdistributions 502, 602 of the present disclosure improve robustness ofthe airfoil 300 without reducing flow capacity or efficiency of therotor 200.

With each of the airfoils 500 formed with the location of local maximumthickness distribution 502 or the location of local maximum thicknessdistribution 602, the airfoils 500 are coupled to the rotor hub 222 toform the rotor 200. With the rotor 200 formed, the rotor 200 isinstalled in the gas turbine engine 100 (FIG. 1). In general, the rotor200 may be incorporated into one or more of the engine sectionsdescribed with regard to FIG. 1 above. For example and additionallyreferring to FIG. 1, the rotor 200 may be incorporated into the fansection 102 such that, as the rotor 200 rotates, the airfoils 500function to draw air into the gas turbine engine 100 with increasedrobustness to foreign object encounters.

In this document, relational terms such as first and second, and thelike may be used solely to distinguish one entity or action from anotherentity or action without necessarily requiring or implying any actualsuch relationship or order between such entities or actions. Numericalordinals such as “first,” “second,” “third,” etc. simply denotedifferent singles of a plurality and do not imply any order or sequenceunless specifically defined by the claim language. The sequence of thetext in any of the claims does not imply that process steps must beperformed in a temporal or logical order according to such sequenceunless it is specifically defined by the language of the claim. Theprocess steps may be interchanged in any order without departing fromthe scope of the invention as long as such an interchange does notcontradict the claim language and is not logically nonsensical.

While at least one exemplary embodiment has been presented in theforegoing detailed description, it should be appreciated that a vastnumber of variations exist. It should also be appreciated that theexemplary embodiment or exemplary embodiments are only examples, and arenot intended to limit the scope, applicability, or configuration of thedisclosure in any way. Rather, the foregoing detailed description willprovide those skilled in the art with a convenient road map forimplementing the exemplary embodiment or exemplary embodiments. Itshould be understood that various changes can be made in the functionand arrangement of elements without departing from the scope of thedisclosure as set forth in the appended claims and the legal equivalentsthereof.

What is claimed is:
 1. A rotor blade for a compressor of a gas turbine engine, comprising: an airfoil extending from a root to a tip and having a leading edge and a trailing edge, with a span that extends from 0% at the root to 100% at the tip and a mean camber line that extends from the leading edge to the trailing edge, the airfoil having a location of local maximum thickness defined as a ratio of a first arc distance along the mean camber line between the leading edge and a position of the local maximum thickness to a total arc distance along the mean camber line from the leading edge to the trailing edge, and a value of the ratio increases from the root to a first position value, decreases from the first position value to a second position value and increases from the second position value to the tip and the first position value is at a spanwise location within 20% to 50% of the span.
 2. The rotor blade of claim 1, wherein the second position value is at a spanwise location within 60% to 90% of the span.
 3. The rotor blade of claim 1, wherein at the tip, the value of the ratio is a third position value that is greater than the first position value, and the third position value is an absolute maximum value of the ratio over the span of the airfoil.
 4. The rotor blade of claim 1, wherein at the tip, the value of the ratio is a third position value, the third position value is less than the first position value, and the first position value is an absolute maximum value of the ratio over the span of the airfoil.
 5. The rotor blade of claim 1, wherein the value of the ratio has a root position value at the root, and the root position value is an absolute minimum value of the ratio over the span of the airfoil.
 6. The rotor blade of claim 1, wherein the value of the ratio has a fourth position value at 10% of the span, and the fourth position value is less than the first position value.
 7. The rotor blade of claim 1, wherein the airfoil further comprises a total camber distribution that increases from the root to a maximum value of total camber between 5% of the span and 20% of the span.
 8. The rotor blade of claim 1, wherein between at least one of the root and the first position value, the first position value and the second position value, and the second position value and the tip, the value of the ratio has a local increase or a local decrease.
 9. A rotor blade for a compressor of a gas turbine engine, comprising: an airfoil extending from a root to a tip and having a leading edge and a trailing edge, with a span that extends from 0% at the root to 100% at the tip and a mean camber line that extends from the leading edge to the trailing edge, the airfoil having a location of local maximum thickness defined as a ratio of a first arc distance along the mean camber line between the leading edge and a position of the local maximum thickness to a total arc distance along the mean camber line from the leading edge to the trailing edge, a value of the ratio increases from a root position value at the root to a first position value, decreases from the first position value to a second position value and increases from the second position value to a third position value at the tip, and the second position value is within 60% to 90% of the span.
 10. The rotor blade of claim 9, wherein the first position value is at a spanwise location within 20% to 50% of the span.
 11. The rotor blade of claim 9, wherein the third position value is less than the first position value, and the first position value is an absolute maximum value of the ratio over the span of the airfoil.
 12. The rotor blade of claim 9, wherein the third position value is greater than the first position value, and the third position value is an absolute maximum value of the ratio over the span of the airfoil.
 13. The rotor blade of claim 9, wherein the root position value is an absolute minimum value of the ratio over the span of the airfoil.
 14. The rotor blade of claim 9, wherein the value of the ratio has a fourth position value at 10% of the span, and the fourth position value is less than the first position value.
 15. A rotor for a compressor of a gas turbine engine, comprising: a hub; and an airfoil extending from a root to a tip and having a leading edge and a trailing edge, with a span that extends from 0% at the root to 100% at the tip and a mean camber line that extends from the leading edge to the trailing edge, the airfoil having a location of local maximum thickness defined as a ratio of a first arc distance along the mean camber line between the leading edge and a position of the local maximum thickness to a total arc distance along the mean camber line from the leading edge to the trailing edge, a value of the ratio increases from a root position value at the root to a first position value, decreases from the first position value to a second position value and increases from the second position value to a third position value at the tip, the root position value is an absolute minimum value of the ratio over the span of the airfoil and the second position value is at a spanwise location within 60% to 90% of the span.
 16. The rotor of claim 15, wherein the first position value is at a spanwise location within 20% to 50% of the span.
 17. The rotor of claim 15, wherein the third position value is less than the first position value and is greater than the second position value, and the first position value is an absolute maximum value of the ratio over the span of the airfoil.
 18. The rotor of claim 15, wherein the third position value is greater than the first position value, and the third position value is an absolute maximum value of the ratio over the span of the airfoil.
 19. The rotor of claim 15, further comprising a plurality of the airfoils, each of the plurality of the airfoils coupled to the hub at the root and spaced apart from adjacent ones of the plurality of the airfoils over the span by a throat dimension defined between the adjacent ones of the plurality of the airfoils, and the throat dimension has a maximum value at a spanwise location between 60% of the span and 90% of the span of the adjacent ones of the plurality of the airfoils.
 20. The rotor of claim 15, wherein the airfoil further comprises a total camber distribution that increases from the root to a maximum value of total camber between 5% of the span and 20% of the span. 